Category:Likelihood Functions

This category contains results about Likelihood Functions.
Definitions specific to this category can be found in Definitions/Likelihood Functions.

Let $\FF$ be a type of probability distribution which has a parameter $\theta$.

Let $X$ be a continuous random variable belonging to a member of $\FF$.

Let the frequency function of $X$ be expressed as $\map f {x, \theta}$, where $x$ is variable and $\theta$ given.

Let $x_1$ be an observation of a variable from $X$.

Then $\theta$ can be regarded as a variable that can be varied so as to specify individual members of $\FF$.

The likelihood function $\map L \theta$ is then defined as:

$\map L \theta := \map f {x_1, \theta}$

regarded as a function of $\theta$ for a given $x_1$.